Computational methods for delay parabolic and time-fractional partial differential equations. (English) Zbl 1204.65114

Rihan, Fathalla A.

Numer. Methods Partial Differ. Equations 26, No. 6, 1556-1571 (2010).

Summary: This article is concerned with \(\vartheta\)-methods for delay parabolic partial differential equations. The methodology is extended to time-fractional-order parabolic partial differential equations in the sense of Caputo. The fully implicit scheme preserves delay-independent asymptotic stability and the solution continuously depends on the time-fractional order. Several numerical examples of interest are included to demonstrate the effectiveness of the method.

Reviewer: Li Changpin (Logan)

MSC:

65M20	Method of lines for initial value and initial-boundary value problems involving PDEs
35R10	Partial functional-differential equations
35R11	Fractional partial differential equations
35K61	Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations
65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs

Keywords:

method of lines; diffusion equations; Runge-Kutta method; \(\vartheta\)-methods; delay parabolic partial differential equations; time-fractional-order parabolic partial differential equations; asymptotic stability; numerical examples

Software:

RADAR5

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